What areas of Belfast are good to go to for dinner/drinks midweek?

Hi All

Heading up to Belfast from Kerry in a couple of weeks (quite a drive!) for a midweek break. We're staying in the city centre, not sure what the hotel is called but it's near the train station and it sounds like a bit of a shit hole so we're not going to be having our dinner and drinks there. I'm trying to book restaurants and I was just wondering if there is a particular area in the city that's lively on Tuesday/Wednesday/Thursday evening? We're not looking for nightclubs because our days are jam packed, just somewhere to have dinner and a couple of drinks after.

Thank you!

Edit: Thank you so much for all of the tips, really appreciate it!